John Malone, chairman of Liberty Media Corp., is considering buying Time Warner Cable if he can structure an offer with enough cash to win over the cable company’s investors. People familiar with the negotiations said Time Warner thinks Malone’s Charter Communications does not have the money, and the cable company isn’t interested in a deal anyway.

AMSTERDAM — John Malone’s international cable business, Liberty Global Inc., has made a new attempt to bolster its footprint in Europe, in the latest consolidation move in the region’s telecom sector.

Dutch cable company Ziggo NV said Wednesday that Liberty Global, which already holds a 28.5 percent stake in the company, made an offer for the shares Liberty doesn’t already own. Ziggo, which has a market capitalization of around $8.4 billion, said it rejected the offer.

“The potential offer was considered inadequate, and there is no certainty that Ziggo will receive any revised offer,” Ziggo said, without giving more details about the bid. “Further announcements will be made if and when relevant.”

Liberty Global didn’t immediately respond to a request for comment.

Douglas County-based Liberty Global has been on a spending spree in recent years and owns broadband networks in a dozen European countries.

The expansion plan comes as Europe’s fragmented telecom industry is expected to undergo a consolidation wave as it wrestles with structural challenges and a weak economy.

“The desire to consolidate appears to have increased,” Goldman Sachs said in a report on the European telecom sector published Wednesday.

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